Thanks for the feedback! I'm in general agreement with your second summary; basically, the properties of triangles end up appearing all over math, so our trig terminology/relationships become generally applicable, especially to circles and other repeating patterns.
One of the best parts of trig is that knowing one little fact (sin(x) = foo) reveals a tremendous number of other ones (inverse sine, get the original angle; then the cosine, tangent, secant, etc.). I'd like to explore some applications (geometric and non), appreciate the suggestion!
I like pointing out to students of classical mechanics that the first year is all about pointing out ramifications of one assumption, one mindlessly simple, underwhelming equation: constant acceleration. If you know a bit of calculus. It goes from being a terrifyingly large amount of memorization and calculation to... "Oh."
One of the best parts of trig is that knowing one little fact (sin(x) = foo) reveals a tremendous number of other ones (inverse sine, get the original angle; then the cosine, tangent, secant, etc.). I'd like to explore some applications (geometric and non), appreciate the suggestion!